一种具有常数时间运算的动态空间有效滤波器
A Dynamic Space-Efficient Filter with Constant Time Operations
摘要：
动态字典是一种数据结构，它维护给定全域中至多$n$的基数集，并支持插入、删除和成员查询。过滤器近似于具有单侧错误的成员资格查询，该单侧错误的发生概率至多为$ε$。目标是获得空间有效的动态滤波器（空间是信息理论下限的$1+o(1)$倍），并以高概率在恒定时间内支持所有操作。设计过滤器的一种方法是简化检索问题。当论域的大小是$n$中的多项式时，只要误差参数$ε$满足$\log(1/ε) = ω(\log\log n)$，该方法就产生空间有效的动态滤波器。对于$\log(1/ε) = O(\log\log n)$的情况下，我们提出了第一个空间有效的动态滤波器的恒定时间操作的最坏情况（whp）。相比之下，Pagh，Pagh，Rao（SODA 2005）的空间高效动态过滤器支持在摊销的期望常数时间内插入和删除。我们的方法采用了经典的减少卡特等人。（STOC 1978）的一种新型的字典建设，支持随机多集。
英文摘要：
A dynamic dictionary is a data structure that maintains sets of cardinality at most $n$ from a given universe and supports insertions, deletions, and membership queries. A filter approximates membership queries with a one-sided error that occurs with probability at most $ε$. The goal is to obtain dynamic filters that are space-efficient (the space is $1+o(1)$ times the information-theoretic lower bound) and support all operations in constant time with high probability. One approach to designing filters is to reduce to the retrieval problem. When the size of the universe is polynomial in $n$, this approach yields a space-efficient dynamic filter as long as the error parameter $ε$ satisfies $\log(1/ε) = ω(\log\log n)$. For the case that $\log(1/ε) = O(\log\log n)$, we present the first space-efficient dynamic filter with constant time operations in the worst case (whp). In contrast, the space-efficient dynamic filter of Pagh, Pagh, Rao (SODA 2005) supports insertions and deletions in amortized expected constant time. Our approach employs the classic reduction of Carter et al. (STOC 1978) on a new type of dictionary construction that supports random multisets.
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